Question

a right triangle has side lengths 9, 40, and 41 as shown below. use these lengths to find cos x, sin x, and tan x.

Explanation:

Step1: Recall cosine formula

$\cos X=\frac{\text{adjacent}}{\text{hypotenuse}}$
In right - triangle $XYZ$, the side adjacent to angle $X$ is $40$ and the hypotenuse is $41$. So, $\cos X = \frac{40}{41}$.

Step2: Recall sine formula

$\sin X=\frac{\text{opposite}}{\text{hypotenuse}}$
The side opposite to angle $X$ is $9$ and the hypotenuse is $41$. So, $\sin X=\frac{9}{41}$.

Step3: Recall tangent formula

$\tan X=\frac{\text{opposite}}{\text{adjacent}}$
The side opposite to angle $X$ is $9$ and the side adjacent to angle $X$ is $40$. So, $\tan X=\frac{9}{40}$.

Answer:

$\cos X=\frac{40}{41}$
$\sin X=\frac{9}{41}$
$\tan X=\frac{9}{40}$